An analysis of the dynamic shear failure resistance of structural metals
Introduction
Shear band formation rather than crack initiation is the principal form of failure for many structural metals under certain dynamic loading conditions. In most applications, this form of failure should be avoided. It is necessary to evaluate the resistance of similar materials to dynamic shear failure in order to achieve maximum structural integrity through design, materials selection and development of more advanced materials. Identifying the factors that determine the susceptibility or resistance of materials to the initiation and propagation of localized shear deformation has clear practical significance. Just as fracture toughness is a measure of material resistance to cracking, there may also be a toughness measure for material resistance to dynamic shear banding. Although the influences of many individual material properties on shear banding, such as strain hardening and rate sensitivity, are understood, no well-developed criterion is available for the comparison of the relative susceptibilities to shear localization of different materials. The difficulty arises partly because different materials have different combinations of properties. The lack of a criterion for the comparison of the relative resistance to shear failure is an issue in the design of structures and the selection of materials.
The occurrence of shear bands at high strain rates is a thermomechanical process driven mainly by heat due to plastic dissipation. Analyses of this phenomenon have either followed mechanics approaches, which are based on descriptions of the thermomechanical response of materials, or materials approaches, which focus on the microscopic evolution associated with the shear band development. The mechanics analyses have yielded understandings on the conditions for the onset and development of shear bands. For example, Clifton, 1980 analyzed the effects of heat conduction and strain rate on the growth of perturbations in deformation fields. Molinari and Clifton, 1987 obtained the critical condition for shear localization in closed form for several idealized models of simple shearing deformation. A sample of related work includes Rogers, 1979 , Bai, 1981, Bai, 1982) , Rogers and Shastry, 1981 , Merzer, 1982 , Freund et al., 1985 , Wright and Walter, 1987 , Grady and Kipp, 1987 , Needleman, 1989 , Shawki and Clifton, 1989 , Batra and Kim, 1991, Batra and Kim, 1992) , Grady, 1992 , Needleman and Tvergaard, 1992 , Nemat-Nasser, 1992 , Shawki, 1992 , Zhib and Aifantis, 1992 , Gioia and Ortiz, 1996 , Kalthoff, 1987 , Mason et al., 1994 , and Zhou et al., 1994, Zhou et al., 1996a,Zhou et al., 1996b, Zhou et al., 1997) . On the other hand, microscopic studies have revealed material deformation, damage and failure mechanisms associated with the localization process. For example, Cho et al., 1990, Cho et al., 1993) analyzed the local temperature profiles inside shear bands in several metals. They also found that rotation and alignment of martensitic laths accompany shear band development. The experiments of Andrade et al., 1994 suggested the occurrence of dynamic recrystallization in copper during shear localization. Other microscopic studies have been reported by e.g. Rogers and Shastry, 1981 , Giovanola, 1988 , Marchand and Duffy, 1988 , Duffy et al., 1992 , Bai et al., 1994 , Ramesh, 1994 , Zurek, 1994 , Meyers et al., 1995 , and Xu et al., 1996 .
Grady, 1994 derived a shear band toughness measure which is indicative of the amount of energy dissipated in propagating shear bands approximated by a one-dimensional model. This quantity is a function of parameters in a simplified material constitutive model and does not account for microscopic damage and ultimate rupture which leads to the eventual failure of materials inside shear bands. Experiments have indicated that the dynamic shear failure of metals is controlled by ductile damage mechanisms as well as their thermomechanical constitutive behavior. Beatty et al., 1991 showed that 4340 steels with the same hardness value but different carbon distributions absorb varying amounts of energy in a split Hopkinson bar experiment. They also identified the importance of grain size on the susceptibility of copper to shear banding, Andrade et al., 1994 . Bai et al., 1994 pointed out that shear band formation in Ti-6Al-4V does not necessarily cause a loss of load-carrying capability. Instead, a loss is observed only after the occurrence of a sudden rupture due to the coalescence of microcracks. Clearly, in order to assess realistically this form of failure, experiments and models accounting for both macroscopic constitutive response and microscopic characterizations are needed.
The objective of this research is to identify, on macro- and microscopic scales, the factors that determine the resistance of materials to dynamic shear failure in the form of shear band formation and eventual rupture and provide an assessment of the relative resistance to this form of failure. The focus is on both the evolution of the load-carrying capacity of these materials during shear band development and associated microscopic changes. The materials studied are structural metals HY-80, HY-100, HSLA-80, 4340VAR and Ti-6Al-4V. These are the materials for many structures and shear banding is the major mode of failure under certain dynamic loading conditions. For example, Hanchak et al., 1993 have demonstrated that shear band formation dominates the dynamic perforation of HY-100 steel. The experiments used in this analysis provide a range of loading rates and superimposed hydrostatic pressures. Deformations can be controlled to occur to various stages of shear localization and failure, allowing shear bands to be frozen at different levels of straining and analyzed using optical and electron microscopy. The experiments will also allow the evolution of the load-carrying capacity of the materials to be obtained and evaluated. Since a range of materials with different macroscopic properties and microstructures are analyzed under similar conditions, the results of this research can contribute to the quantification of the shear band toughness of materials.
Section snippets
Materials
The four structural steels and one titanium alloy studied are listed in Table 1 along with their chemical compositions. HY-80 and HY-100 are carbon steels with different levels of yield strength resulting from their different carbon and magnesium contents. HSLA-80 is a low alloy substitute of HY-80 with a lower amount of carbon and an increased amount of magnesium. The 4340VAR steel is a low alloy steel. Ti-6Al-4V is a high temperature titanium alloy. The heat treatment conditions and the
Dynamic Shear Failure Experiment
An experimental configuration involving a hat specimen geometry is used. The geometry of the specimen is illustrated in Fig. 3. The specimens are machined from one inch plates, with their axes parallel to the plate normal. This experiment is used to subject the materials to nominal shear deformations in the strain rate range of 102–104 s−1. This configuration was first used by Beatty et al., 1991 , Andrade et al., 1994 , and Meyers et al., 1995 to analyze the shear deformation of a 4340 steel
Dynamic constitutive response
The dynamic constitutive behaviors of the materials are analyzed using the same split Hopkinson compression bar apparatus. The specimen is a cylinder 3 mm in diameter and 3 mm in length. The stress-strain curves for the five materials over the strain rate range of 102–104 s−1 are shown in Fig. 4 (a) – (e) . A comparison of the dynamic responses of the materials for similar strain rates between 2.1–2.4×104 s−1 is given in Fig. 4 ( f) . The curves show that like their similar quasistatic yield
Discussion and Summary
Although it is based on an approximate characterization of the thermomechanical response and a one-dimensional deformation model, the shear band dissipation energy derived by Grady, 1994 allows the energy dissipated per unit area of shear band growth for different materials to be estimated and compared. This shear band dissipation energy iswhere ρ is density, χ is thermal diffusion coefficient, α is a thermal softening coefficient, c is specific heat, τy is the flow
Acknowledgements
Support from the Office of Naval Research through grant No. N00014-96-1-1195 to Georgia Institute of Technology is gratefully acknowledged.
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